Springs and spring-like objects have been made from fiber-reinforced composites by workers in several fields of endeavor. Such composites typically include reinforcing fibers in a thermosetting resin matrix. One well-known such family of composite materials is Owens-Corning.TM. Fiberglass.RTM.. Flat springs such as fiberglass fishing rods and hunting bows have long been in use, and at least one American automobile has been produced with a glass-reinforced transverse leaf spring for some time. U.S. Pat. Nos. 4,468,014 to Strong and 4,718,693 to Booher teach variations of such glass-reinforced composite leaf springs. Torsional springs made of reinforced composites have also been the subject of efforts by others. U.S. Pat. No. 2,812,936 to Setz, hereinafter '936, details one such effort using alternating, or cross-woven helical windings.
Composite helical springs have also been patented. U.S. Pat. Nos. 4,260,143 and 4,380,483 to Kliger, hereinafter '143 and '483, teach composite helical springs made with fibers braided so that they lie roughly 45.degree. from the axis of the main helix, with successive layers alternating their direction of twist. Other composite helical springs have been made with the reinforcing fibers parallel (or nearly so) to the main helix of the spring. One such spring, taught by U.S. Pat. No. 4,473,217 to Hashimoto, features a bundle of fibers which is twisted into a rod-shaped bundle, saturated with a thermosetting resin, and the resultant bundle formed into a helical spring. Each of these designs provide superior function and light weight over prior art metallic springs and spring-like objects, but fails to optimize the performance of such composite springs by failing to recognize some of the forces inherent in spring design, and optimizing the orientation of the reinforcing fibers.
Hashimoto, in stating that ". . . the elastic characteristics of the rod-shaped fiber bundle have varied due to the amount of twisting, it is necessary to determine the amount of twisting the rod-shaped fiber bundle according to the desired elastic characteristic of the fiber bundle. (sic)" teaches modification of core twist to change the elastic characteristics of the core, and thus presumably the resultant spring. This teaching fails to appreciate several important points: first, the core of the spring has significantly less effect on the elastic characteristics of the resultant spring than do the reinforcing fibers on the periphery of the cross section, hereafter referred to as the cladding. Next, with respect to the core, an even more important factor for determining the degree and direction of core twist is the minimization of shear stresses on the reinforcing fibers thereof. The core of a spring wound as tightly, for instance, as illustrated in FIGS. 2 and 3 of the Hashimoto reference will impose significant shear stresses on the core reinforcing fibers, resulting in increased internal friction and decreased service life. Further, these shear stresses are amplified when the cladding is wound with the opposite sense of the core twist. Finally, excessive core twist increases the difficulty, and hence cost, of manufacturing such a spring.
The prior art composite torsion and helical designs present several areas for improvement. First, the braided or cross-woven designs require that the reinforcing fibers (hereinafter "fibers") be wound in both directions around the helical bundle. This means that, in a given application, many of the fibers, particularly those in compression, will not carry load well. Secondly, pertaining to braided designs, the fibers cannot be aligned with the forces acting on them, as being braided, those fibers are woven about one another and are hence always crooked. This makes the fibers loaded in compression tend to instability and buckling. Finally, the angle at which the reinforcing fibers is wound in the spring has significant impact on the properties of that spring. The prior art does not teach a methodology to optimize this wind angle.
An analysis of the forces generally operating on springs will help to provide a solution to the previously discussed disadvantages with prior art composite torsion and helical spring designs, as well as realizing further benefits accruing from an optimally designed composite spring.
Compression, tension and torsion-bar springs are typically cylindrical in section. Compression and tension springs are generally helical in form. Torsion bars are generally straight. The cross-section of each of these types of spring is stressed mostly in shear by torsion loading, with generally much smaller stresses caused by bulk shear and tension or compression. It follows then that the greatest shear strain, and thus stress, occurs at the outermost portion of the section, and that the inner portions are little stressed and contribute little to the spring's ability to store energy.
From the preceding, we can deduce that most of the energy stored in a composite torsional or helical spring is stored in the outermost fiber layers, and that fibers closest to the center of the cross-section store little, if any useful energy. These fibers, in prior art composite springs, serve primarily to maintain the form of the spring and do little actual work, or store little actual energy.
The helical springs which use fibers roughly parallel to the main helix, such as taught by '217, are useful as helical torsion springs, where the spring section is actually loaded in bending. However, they are not optimally effective as tension or compression springs, since the torsion on these spring sections cannot be reacted by the fibers, which would be perpendicular to the applied stress.
Springs are often loaded either wholly or predominantly in one direction: tension, compression, or unidirectional torsion. This fact provides an insight into spring design apparently overlooked by the prior art: namely, that in many applications it is not necessary that the spring be capable of both tension and compression loading. By optimizing the orientation of the reinforcing fibers, it will be shown that such springs possess advantages over prior art metallic and composite springs. These advantages include improvements in physical size, density and reduction of shock transmitted through the spring as a wave force, elastic potential energy (both on a per-unit-volume and on a per-unit-weight basis), surge frequency, and maximum axial velocity.
The abstract purpose of a spring is to store energy, imparted to the spring in the form of work, as elastic potential that can be used to restore the spring, and the using function, to its original state. In cases where it is desirable to minimize the size, weight or dynamic-surge-loading of a spring, the material properties that are most important are working strength, elastic modulus and mass density. The energy per unit volume in any spring is proportional to the working strength squared divided by the elastic modulus, or ##EQU1## where U=maximum elastic potential energy
V=active spring volume PA1 S=working strength of the spring material PA1 E=spring material elastic modulus. PA1 .rho.=spring material density.
and
The energy per unit weight in a spring is the energy per unit volume, above, divided by the density of the spring, or ##EQU2## where W=spring weight
and
On both energy per-unit volume and per-unit-weight bases, it becomes apparent that the maximum elastic potential energy of a given spring increases with a decrease in the elastic modulus of the material forming the spring. Further gains are made, on an energy per-unit-weight basis, with every reduction of spring material density.
By combining a design which, during a given application, places a significantly greater proportion of spring mass in direct tension by optimizing fiber orientation, with modern technical reinforcing fibers, unexpected gains in elastic energy and other static and dynamic spring functions are possible. A careful selection of the materials utilized in forming the composite yields increases in several areas of spring performance.
Once such improvement is in the area of the specific energy (either per-unit-weight or per-unit-volume) which the spring is capable of storing. Prior art spring materials include homogeneous metal alloys, helical wire springs made with multiple strands wound helically together to provide damping via coulomb friction between the strands, or the previously discussed composite materials. Some of the more important properties for materials under consideration for inclusion in composite spring design are summarized in the following table:
__________________________________________________________________________ Tensile Tensile Strain Energy Strain Energy by Material Strength Modulus Density by Volume Weight __________________________________________________________________________ Steel 250,000 psi 30 .times. 10.sup.6 psi .283 lb.sub.m /in.sup.3 1,042 in-lb.sub.f /in.sup.3 3,681 in-lb.sub.f /lb.sub.m Titanium Alloy 230,000 14.8 .times. 10.sup.6 .176 1,787 10,154 High-Strength 660,000 37 .times. 10.sup.6 .065 5,886 90,561 Graphite Fiber S-2 Glass.sup.a 600,000 13 .times. 10.sup.6 .089 13,846 155,575 Fiber E Glass Fiber 375,000 10 .times. 10.sup.6 .093 7,031 75,604 Kevlar 29.sup.b Aramid 525,000 12 .times. 10.sup.6 .052 11,484 220,853 Fiber Dacron.sup.b Fiber 162,500 2 .times. 10.sup.6 .050 6,602 132,031 __________________________________________________________________________ .sup.a S2 Glass is a registered trademark of Owens Corning Fiberglas Corp .sup.b Kelvar and Dacron are registered trademarks of E. I. DuPont de Nemours & Co., Inc.
It is obvious from the above table that all of the materials, other than the metals, are superior to the metals in their ability to store elastic potential energy both on a per-unit-volume and on a per-unit-weight basis. Steel, which is the most common spring material, can store only one sixtieth as much energy per unit weight as can some aramid fibers and less than one thirteenth as much per unit volume as the best glass fibers.
At this time, no practical composite can be made with its entire weight and volume made up of nothing but high-strength filaments. Until this becomes possible, in order to bond the fibers into an integral whole, some form of bonding agent or matrix is typically used. Such matrices are typically homomeric or polymeric plastics and take a variety of forms well known in the art, including thermosetting epoxy, polyimide, polyether ether ketone, and polyester resins. The necessity for these matrices decreases the percentage of the fibers in the composite, or volume fiber loading.
Assuming that 50% volume fiber loading can be achieved in a unidirectionally wound composite spring where all the fibers are properly loaded, and that the appropriately compliant polymer bonding matrix has a density of 0.05 lb.sub.m /in.sup.3, the relevant properties for the resulting composite spring would be as shown in the following table:
__________________________________________________________________________ Reenforcing Tensile Tensile Strain Energy Strain Energy by Material Strength Modulus Density by Volume Weight __________________________________________________________________________ High-Strength 330,000 psi 18.5 .times. 10.sup.6 psi .0575 lb.sub.m /in.sup.3 2,943 in-lb.sub.f /in.sup.3 51,187 in-lb.sub.f /lb.sub.m Graphite Fiber S-2 Glass.sup.a 300,000 6.5 .times. 10.sup.6 .0695 6,923 99,613 Fiber E Glass Fiber 187,500 5 .times. 10.sup.6 .0715 3,516 49,170 Kevlar 29.sup.b Aramid 262,500 6 .times. 10.sup.6 .051 5,742 112,592 Fiber Dacron.sup.b Fiber 81,250 1 .times. 10.sup.6 .050 3,301 66,016 __________________________________________________________________________ .sup.a S2 Glass is a registered trademark of Owens Corning Fiberglas Corp .sup.b Kevlar and Dacron are registered trademarks of E. I. DuPont de Nemours & Co., Inc.
Allowing for fifty percent by volume of the composite being matrix, the above tabulated results demonstrate that composite springs utilizing the above-identified fibers are 13 to 30 times lighter than steel, and 2.8 to 6.6 times smaller in terms of volume. Improvements of this magnitude are therefore seen to be achievable if a fiber-reinforced composite, using advanced fibers such as those recited above, can be optimized as an effective spring.
Another advantage attainable in an optimally designed fiber-reinforced composite helical spring is an increase in maximum velocity of motion along the spring's axis, or axial velocity. Many helical spring applications require that one or more points (usually one end) on a spring move at high speed, either episodically or repetitively. Examples include: valve springs in reciprocating engines, which can sometimes be subjected to high end speeds in a periodic fashion; shock and impact attenuation systems, as in automotive suspension or weapons system recoil attenuation and counter-recoil systems, which can impose a high velocity on a spring end in either a periodic or episodic fashion; and finally dart guns, pinball machines and percussion primer firing mechanisms (springs for firing pins) which typically operate episodically compared to the time scale of spring unloading. All of these applications benefit from an increase in axial velocity resulting from the lighter weight and lower elastic modulus (relative to working strength) of composite materials.
It should be noted that any change in the axial velocity of an end of a spring creates an elastic wave which travels along the length of the spring. The change in local axial force that is generated by an imposed change in velocity is as follows: ##EQU3## where .DELTA.F is the change in axial force on the spring, .DELTA.V is the imposed change in velocity of the end of the spring, d is the "wire" diameter, r is the radius of the spring helix, G is the effective elastic shear modulus of the material and .rho. is the average mass density of the spring material.
For materials of similar effective working shear strength, a spring can be constructed for a given maximum static load and spring rate from each of said materials with the same wire diameter and helix radius: the differences in elastic modulus can be compensated for by making the springs with more or less coils to correspond with greater or lesser elastic moduli, respectively. Since we can compare springs of similar local geometry, it is apparent from the above equation that selecting spring materials having lesser elastic modulus and/or lower mass density will result in a spring have a smaller wave (dynamic) force for a given imposed velocity change. This results in less stress on the spring itself during use, and reduces any shock transmitted through the spring as a wave force.
It is also the case that springs made from lighter and less stiff materials experience less stress for a given imposed velocity change, as is apparent from the following equation: ##EQU4## where .tau..sub.max is the approximate maximum shear stress in the "wire," and the other variables are as above. From this it is apparent that the maximum speed to which a given material spring can launch an object is ##EQU5## which implies that a Kevlar-reinforced composite spring should be able to launch a light object at a speed between three and four times that achievable with the best steel spring.
By utilizing an optimally designed composite spring having a low shear modulus and density, an additional advantage obtains. In springs that are subjected to periodic motion, it is well known that stresses can become excessive and motion unpredictable if the dynamic waves generated in the spring resonate at or near the frequency of the imposed periodic motion (as in valve springs in high speed internal combustion engines). Since such applications typically run at a range of frequencies, it is common practice to design the system (including the springs) so that the highest frequency of imposed motion is below the lowest surging frequency of the springs used. This can impose a maximum velocity on the system which is thus limited by spring performance. Because the equation for the lowest surge frequency of a helical spring is ##EQU6## where k is the spring force gradient or spring rate (which is usually prescribed to meet the demands of a particular application), it becomes apparent that by selecting materials having lower shear modulus and density, i.e. high performance, optimally wound composites, the resultant springs formed therefrom exhibit an increased surge frequency. Such springs would therefore be useable at higher speeds and over a broader range of applications.
The potential exists then to significantly improve the performance, in several important areas, of prior art helical and torsion metallic and composite springs. These improvements include decreases in physical size, density, and shock transmitted through the spring as a wave force, and increases in elastic potential energy (both on a per-unit-volume and on a per-unit-weight basis), surge frequency, and axial velocity.
The foregoing discussion demonstrates that, in addition to enabling the use of smaller and lighter weight springs in static applications, these springs should also be superior in all dynamic respects. In suspension and recoil attenuation systems, less surge force will be transmitted from the moving end to the fixed end of a spring when it is dynamically loaded. In mass launching systems, masses can be launched to higher speeds. In periodically loaded applications, springs can be safely used at higher frequencies, allowing higher operating speeds for the use application. Finally, in all dynamic applications, the induced dynamic stress can be less for a given imposed end velocity change, which should yield greater spring life or greater design flexibility in all dynamic applications.